PreCalculus

posted by .

Linear Programming/Systems of Inequalities

The photocopying machine in a school office is made available to teachers between the hours of 3pm and 4pm. Mr. Grim and Mrs. Grump each have 10 minutes of copying to do each day. If theyh each enter the office at points in the available hour, what is the probability that one of them will have to wait while the other finishes copying?

Hi Sam. Welcome to Jiskha!

Draw yourself an x,y plot with both axes running from 0 to 50 minutes, representing the times that Grim (x) and Grump (y) might enter the room, measured from 3 PM. Assume those times are randomly distributed. The area of (x,y) space where |x-y| < 10 is the region where one or the other person is going to have to wait.

The probability that one of them will have to wait is the ratio or the area of a diagonal region between the lines x = y + 10 and x = y - 10, to the area of the 50 x 50 square. I get that ratio to be
1 - (2*0.5*40*40)/(50*50) = 1 - 16/25 = 9/25

The number (2*0.5*40*40)/(50*50) = 16/25 is the fraction of x,y space where no waiting is required, and is the ratio of the sum or two right-triangular areas to that of the 50 x 50 square

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. linear programming app

    write the constraints as linear inequalities and identify all variables used. A canoe requires 8 hours of fabrication and a rowboat 5 hours. The fabrication department has at most 110 hours of labor available each week
  2. linear programming app

    solve this linear programming problem; A chain saw requires 4 hours of assembly and a wood chipper 6 hours. A maximum of 48 hours of assembly time is available. The profit is $150 on a chain saw and $220 on a chipper. How many of each …
  3. Algebra 2 (Linear Programming)

    A bicycle builder makes two models. The basic model requires 2 hours of frame construction, 4 hours of assembly, and 1 hour of finishing. The deluxe model requires 3 hours of frame construction, 3 hours of assembly, and 2 hours of …
  4. Algebra 2 (Linear Programming)

    Part A requires 4 hours per unit on a lathe and 3 hours per unit on a milling machine. Part B requires 2 hours per unit on a lathe and 5 hours per unit on a milling machine. 52 hours are available on the lathe and 60 hours are available …
  5. Algebra 2

    A factory is producing DVD and Blu Ray discs. For each case of DVDs they make $180 profit. For each case of Blu Ray they make $250. The DVDs take 3 minutes of machine time and 7 minutes of labor. The Blu Rays take 4 minutes of machine …
  6. Algebra 1

    How many solution sets do systems of linear inequalities have?
  7. math

    How many solution sets do systems of linear inequalities have?
  8. Algebra 1A

    How many solution sets do systems of linear inequalities have?
  9. Linear Programming

    We produce two products: product 1 and product 2 on two machines (machine 1 and machine 2). The number of hours of machine time and labor depends on the machine and the product as shown in Table 64. The cost of producing a unit of …
  10. Math

    Machine A was able to finish copying a set of document in 36 minutes. Machine B was brought in to work together with machine A to finish copying the document in 20 minutes. How long would it take machine B to finish copying the document …

More Similar Questions